Topological phase in a $d_{x^2-y^2}+(p+ip)$ superconductor in presence of spin-density-wave

Abstract: We consider a mean-field Hamiltonian for a $d_{x^2-y^2}+(p+ip)$ superconductor(SC) in presence of spin-density-wave(SDW) order. This is due to the fact that the non-commutativity of any two orders produces the third one. The energy spectrum of such a Hamiltonian is shown to be gapped and it yields a topological phase in addition to the conventional one. A phase diagram characterizing different topological phases is construted. The Chern numbers and hence the nature of the topological phases are determined. The edge state spectrum and the possibility of whether the vortex state harbouring the zero modes are discussed.